Angular acceleration of a bar on a hinge

In summary, the problem involves a bar on a hinge starting from rest and rotating with an angular acceleration of \alpha=(10+6t) rad/s2. The task is to determine the angle in radians the bar turns in the first 4 seconds, which can be solved by integrating the angular acceleration with respect to time twice and using boundary conditions.
  • #1
mickellowery
69
0

Homework Statement


A bar on a hinge starts from rest and rotates with [tex]\alpha[/tex]=(10+6t) rad/s2 t is in seconds. Determine the angle in radians the bar turns in the first 4 seconds.


Homework Equations


I'm a little stumped how to get this one started. I assume i need to get it from angular acceleration to angular displacement, but I'm not exactly sure how to do that. So do I have to integrate it with respect to time twice?


The Attempt at a Solution

 
Physics news on Phys.org
  • #2
That's right. Remember to use constants of integration/ boundary conditions in general (although it should make no difference in this case).
 

Related to Angular acceleration of a bar on a hinge

What is angular acceleration?

Angular acceleration is the rate at which the angular velocity of an object changes over time. It is measured in radians per second squared (rad/s²) or degrees per second squared (deg/s²).

How is angular acceleration different from linear acceleration?

Angular acceleration refers to the change in rotational speed of an object, while linear acceleration refers to the change in linear speed or velocity. Angular acceleration is measured in terms of rotation, while linear acceleration is measured in terms of distance traveled.

How is the angular acceleration of a bar on a hinge calculated?

The angular acceleration of a bar on a hinge can be calculated by dividing the torque applied to the bar by its moment of inertia. This can be represented by the equation α = τ / I, where α is the angular acceleration, τ is the torque, and I is the moment of inertia of the bar.

What factors can affect the angular acceleration of a bar on a hinge?

The angular acceleration of a bar on a hinge can be affected by the magnitude of the applied torque, the moment of inertia of the bar, and the angle at which the torque is applied. Other factors such as friction, air resistance, and external forces can also play a role.

How does the angular acceleration of a bar on a hinge relate to its motion?

The angular acceleration of a bar on a hinge is directly proportional to the net torque applied to the bar. This means that the greater the torque, the greater the angular acceleration and the faster the bar will rotate. Conversely, if no torque is applied, the bar will not experience any angular acceleration and will remain at rest.

Similar threads

  • Introductory Physics Homework Help
Replies
7
Views
799
  • Introductory Physics Homework Help
Replies
12
Views
1K
  • Introductory Physics Homework Help
Replies
8
Views
1K
  • Introductory Physics Homework Help
Replies
9
Views
502
  • Introductory Physics Homework Help
Replies
7
Views
431
  • Introductory Physics Homework Help
Replies
3
Views
1K
  • Introductory Physics Homework Help
Replies
21
Views
2K
Replies
7
Views
346
  • Introductory Physics Homework Help
Replies
7
Views
2K
  • Introductory Physics Homework Help
Replies
1
Views
1K
Back
Top